KANT'S CRITIQUE OF TELEOLOGY IN BIOLOGICAL EXPLANATION

Concept of Infinity 91
In order better to assess Kant's arguments for the refutation of the
antithesis I shall also introduce the most influential critical interpretation
of Kant's argument, which attempts to refute Kant's refutations.
To refute the antithesis, Kant adduces (in the "proof" of the
thesis) the following argument:
If we assume that the world has no beginning in time, then up to every given
moment an eternity has elapsed, and there has passed away in the world an
infinite series of successive states of things. Now the infinity of a series
consists in the fact that it can never be completed through successive synthesis.
It thus follows that it is impossible for an infinite world-series to
have passed away ... (B454)
The standard objection now made by contemporary commentators
was first introduced by Schopenhauer, given its most lucid articulation
by Russell, and popularized by Strawson and Bennett. Strawson
presents Kant's arguments as follows: 42
[Suppose] that for as long as the world has existed a clock has been ticking
at regular intervals. Then the argument goes as follows. If we assume that
the world has no beginning, but has existed for an infinite time, then it follows
that up to present moment, or up to any previous historical moment, an
infinite number of ticks has occurred, an infinite series of ticks has been
completed. But this, by the very nature of an infinite series, is impossible.
Strawson objects, that an infinite temporal series of discrete events
out of the past is only impossible if we not only assume an end in the
present but also implicitly insinuate a beginning sometime in the
past. In this case we would be asserting infinitely many discrete
units between two given points, which is in fact impossible; but the
argument was supposed to prove that there was no beginning of the
world. An infinite series must be open ended, but it can be open on
either end. It seems clear that Kant has confused the end of the real
progress of world history with that of the mental regress back in
time.
Kant's own further arguments, however, deal with the difference
between an infinite and an indefinite regress into the past. He
writes:
For the solution, therefore, of the first cosmological problem we have only
to decide whether in the regress to the unconditioned magnitude of the
universe, in time and space, this never limited ascent can be called a regress
to infinity, or only an indeterminately continued regress (in indefinitum).
(B546; emphasis PM)
42 Strawson, Bounds, pp. 176f; cf. also Bennett, Dialectic, p. 119.